A339438 - OEIS

%I #11 Feb 06 2021 22:08:32

%S 6,10,14,15,20,21,24,26,33,34,35,38,40,44,46,51,52,55,57,58,63,65,74,

%T 76,85,86,88,90,92,93,96,111,117,118,123,124,135,136,141,143,145,147,

%U 150,153,155,158,161,164,166,172,177,178,180,184,185,194,198,201,203,205,206,207,208,209,215,221

%N Composite numbers k such that k + A339436(k) is prime.

%C If n = p_1 * ... * p_m with primes p_i <= p_{i+1}, then p_1 + p_1*p_2 + ... + p_1*p_2*...*p_m + p2*...*p_m + ... + p_m is prime.

%H Robert Israel, <a href="/A339438/b339438.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5)=20 is a term because 20=2*2*5 and 2+2*2+2*2*5+2*5+5 = 41 is prime.

%p filter:= proc(n) local L,m;

%p   L:= sort(map(t -> t[1]$t[2],ifactors(n)[2]));

%p   m:= nops(L);

%p   if m=1 then return false fi;

%p   isprime(n + add(mul(L[i],i=1..j)+mul(L[i],i=j+1..m),j=1..m-1))

%p end proc:

%p select(filter, [$4..300]);

%Y Includes A088709.

%Y Cf. A339436, A339437.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 04 2020